I'm fairly sure it means something like, "I think that so much, when people offer to do something for me out of good will, I think "It's inexcusable that they would go out of their way to do something for a person like me", and frantically continue to refuse those favors.

But I like to put sentences into Anki and if it's somewhat off, some part of my Japanese will be "off" for a long time, so I wanted to check.

私は means the subject is the narrator in the first sentence though. There's also a detailed story later in the text, which I don't think one could write about another person, and more 私は at the beginning of sentences... Could he mean that he thinks he looks like he worries about not bothering anyone to other people?

Feels strange to argue when asking for help, but I would use:

"Seemingly thinking it over thoroughly, I continued to refuse people's good intentions, saying 'You shouldn't do something like that for someone like me'.

I suppose you're right. I was thinking in terms of politeness rather than strength of inclination (i.e 'refuse' sounds more abrasive than 'decline') because the speaker is refusing for the sake of being polite. But in terms of the English translation 'refuse' works better perhaps.

Like Richvhさん said よう makes it sounds like another person appears to be 思いすぎている ..but I'm going to assume this person means 'it would appear that I am thinking too much'

note that 思い here is the person's care (thought) to not bother their friends, rather than 'thinking too much about this problem'